A filter of the abovementioned general type shall be referred to hereinafter as a rank filter, wherein R=1 corresponds to the maximum (or greatest or largest) of the input values and R=K corresponds to the minimum (or smallest) of the input values. A one-dimensional rank filter computes at each moment m=L·n the R-maximum (i.e. Rth-greatest or Rth-largest) value of K consecutive values of an input signal x(n); for L=1 it is a filter without decimation, i.e. without any reduction of the sampling rate, for L>1 this is a filter with decimation. Analogously, a multidimensional rank filter detects the Rth-largest value of K adjacent values of a multidimensional signal. It goes without saying that here the Rth-largest input value corresponds to the (K−R)-minimum (i.e. (K−R)th-smallest) input value, so that synonymously the method also comprises the determination of an x-minimum (i.e. xth-smallest) input value, in which the Rth-largest value is searched for simply with R=K−x.
A special case of such a rank filter is a median filter. The median of an odd number K of input values is middle value among the several values, i.e. the (K+1)/2-smallest value or, equivalently, the (K+1)/2-largest value, which in general is different from the mean or average value. For instance, for the five values 5, 3, 2, 79 and 1, the median is the value 3, while the mean or average of these numbers is 18.
Digital filters of this type serve for signal processing of acquired input values, for example, the processing of image data or distance measuring signals, in particular also reflection signals of pulses reflected in a target area, whereby optical waves, preferably in the infrared region, radar waves or ultrasonic waves can be used. Implementing such a non-linear filter is only possible in the digital range.
For implementing such filters algorithms are known, which most often are based on sorting methods, which require extensive calculation or they are based on histogram methods, which require high storage requirements, and which are in general more suitable for software than hardware implementation.